Add or subtract the same value from both sides of the equation

Oct 13, 2025 by magicalceylontours.com 66 views

Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable to find its value. In this article, we will focus on solving a simple linear equation of the form 290 - x = 129. We will break down the solution into step-by-step instructions and provide a clear explanation of each step.

Understanding the Equation

The given equation is 290 - x = 129. Our goal is to isolate the variable x and find its value. To do this, we need to get rid of the negative term -x by adding x to both sides of the equation.

Step 1: Add x to Both Sides of the Equation

To isolate x, we need to get rid of the negative term -x. We can do this by adding x to both sides of the equation. This will cancel out the -x term and leave us with a simpler equation.

290 - x + x = 129 + x

Step 2: Simplify the Equation

After adding x to both sides of the equation, we can simplify the left-hand side of the equation by combining like terms.

290 = 129 + x

Step 3: Subtract 129 from Both Sides of the Equation

To isolate x, we need to get rid of the constant term 129. We can do this by subtracting 129 from both sides of the equation.

290 - 129 = 129 + x - 129

Step 4: Simplify the Equation

After subtracting 129 from both sides of the equation, we can simplify the left-hand side of the equation by combining like terms.

161 = x

Conclusion

In this article, we solved a simple linear equation of the form 290 - x = 129. We broke down the solution into step-by-step instructions and provided a clear explanation of each step. By following these steps, we were able to isolate the variable x and find its value.

Tips and Tricks for Solving Linear Equations

Here are some tips and tricks for solving linear equations:

Use inverse operations: To isolate the variable, use inverse operations such as addition, subtraction, multiplication, and division.
Get rid of negative terms: To isolate the variable, get rid of negative terms by adding or subtracting the same value from both sides of the equation.
Combine like terms: To simplify the equation, combine like terms by adding or subtracting the same value from both sides of the equation.
Check your work: To ensure that your solution is correct, check your work by plugging the value of the variable back into the original equation.

Real-World Applications of Solving Linear Equations

Solving linear equations has many real-world applications in fields such as science, engineering, economics, and finance. Here are a few examples:

Physics: In physics, linear equations are used to describe the motion of objects. For example, the equation v = u + at describes the velocity of an object as a function of time.
Engineering: In engineering, linear equations are used to design and optimize systems. For example, the equation P = IV describes the power of an electrical circuit as a function of voltage and current.
Economics: In economics, linear equations are used to model economic systems. For example, the equation C = a + bP describes the demand for a product as a function of price.
Finance: In finance, linear equations are used to model financial systems. For example, the equation A = P(1 + r)^n describes the future value of an investment as a function of principal, interest rate, and time.

Conclusion

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable to find its value. In this article, we solved a simple linear equation of the form 290 - x = 129. We broke down the solution into step-by-step instructions and provided a clear explanation of each step. By following these steps, we were able to isolate the variable x and find its value. Solving linear equations has many real-world applications in fields such as science, engineering, economics, and finance.

Introduction

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable to find its value. In our previous article, we solved a simple linear equation of the form 290 - x = 129. In this article, we will provide a Q&A guide to help you understand and apply the concepts of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form ax + b = c, where a, b, and c are constants.

Q: What is the goal of solving a linear equation?

A: The goal of solving a linear equation is to isolate the variable and find its value. This involves getting rid of the constant term and the coefficient of the variable.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

Add or subtract the same value from both sides of the equation: To get rid of the constant term, add or subtract the same value from both sides of the equation.
Combine like terms: To simplify the equation, combine like terms by adding or subtracting the same value from both sides of the equation.
Check your work: To ensure that your solution is correct, check your work by plugging the value of the variable back into the original equation.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when solving linear equations.
Not combining like terms: Make sure to combine like terms by adding or subtracting the same value from both sides of the equation.
Not checking your work: Make sure to check your work by plugging the value of the variable back into the original equation.

Q: How do I know if my solution is correct?

A: To ensure that your solution is correct, check your work by plugging the value of the variable back into the original equation. If the equation is true, then your solution is correct.

Q: What are some real-world applications of solving linear equations?

A: Solving linear equations has many real-world applications in fields such as science, engineering, economics, and finance. Some examples include:

Physics: In physics, linear equations are used to describe the motion of objects. For example, the equation v = u + at describes the velocity of an object as a function of time.
Engineering: In engineering, linear equations are used to design and optimize systems. For example, the equation P = IV describes the power of an electrical circuit as a function of voltage and current.
Economics: In economics, linear equations are used to model economic systems. For example, the equation C = a + bP describes the demand for a product as a function of price.
Finance: In finance, linear equations are used to model financial systems. For example, the equation A = P(1 + r)^n describes the future value of an investment as a function of principal, interest rate, and time.

Q: Can I use technology to solve linear equations?

A: Yes, you can use technology to solve linear equations. Many calculators and computer software programs have built-in functions to solve linear equations.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

Use inverse operations: To isolate the variable, use inverse operations such as addition, subtraction, multiplication, and division.
Get rid of negative terms: To isolate the variable, get rid of negative terms by adding or subtracting the same value from both sides of the equation.
Combine like terms: To simplify the equation, combine like terms by adding or subtracting the same value from both sides of the equation.
Check your work: To ensure that your solution is correct, check your work by plugging the value of the variable back into the original equation.

Conclusion

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable to find its value. In this article, we provided a Q&A guide to help you understand and apply the concepts of solving linear equations. By following the steps and tips outlined in this article, you will be able to solve linear equations with confidence and accuracy.